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      "source": [
        "from torchvision import datasets\n",
        "import torch\n",
        "data_folder = '~/data/FMNIST' # This can be any directory you want to \n",
        "# download FMNIST to\n",
        "fmnist = datasets.FashionMNIST(data_folder, download=True, train=True)\n",
        "tr_images = fmnist.data\n",
        "tr_targets = fmnist.targets"
      ],
      "execution_count": null,
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        {
          "output_type": "stream",
          "text": [
            "Downloading http://fashion-mnist.s3-website.eu-central-1.amazonaws.com/train-images-idx3-ubyte.gz to /root/data/FMNIST/FashionMNIST/raw/train-images-idx3-ubyte.gz\n"
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          "text": [
            "Extracting /root/data/FMNIST/FashionMNIST/raw/train-images-idx3-ubyte.gz to /root/data/FMNIST/FashionMNIST/raw\n",
            "Downloading http://fashion-mnist.s3-website.eu-central-1.amazonaws.com/train-labels-idx1-ubyte.gz to /root/data/FMNIST/FashionMNIST/raw/train-labels-idx1-ubyte.gz\n"
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          "text": [
            "Extracting /root/data/FMNIST/FashionMNIST/raw/train-labels-idx1-ubyte.gz to /root/data/FMNIST/FashionMNIST/raw\n",
            "Downloading http://fashion-mnist.s3-website.eu-central-1.amazonaws.com/t10k-images-idx3-ubyte.gz to /root/data/FMNIST/FashionMNIST/raw/t10k-images-idx3-ubyte.gz\n"
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          "text": [
            "Extracting /root/data/FMNIST/FashionMNIST/raw/t10k-images-idx3-ubyte.gz to /root/data/FMNIST/FashionMNIST/raw\n",
            "Downloading http://fashion-mnist.s3-website.eu-central-1.amazonaws.com/t10k-labels-idx1-ubyte.gz to /root/data/FMNIST/FashionMNIST/raw/t10k-labels-idx1-ubyte.gz\n",
            "\n",
            "\n"
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          "text": [
            "Extracting /root/data/FMNIST/FashionMNIST/raw/t10k-labels-idx1-ubyte.gz to /root/data/FMNIST/FashionMNIST/raw\n",
            "Processing...\n",
            "Done!\n",
            "\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "stream",
          "text": [
            "/usr/local/lib/python3.6/dist-packages/torchvision/datasets/mnist.py:469: UserWarning: The given NumPy array is not writeable, and PyTorch does not support non-writeable tensors. This means you can write to the underlying (supposedly non-writeable) NumPy array using the tensor. You may want to copy the array to protect its data or make it writeable before converting it to a tensor. This type of warning will be suppressed for the rest of this program. (Triggered internally at  /pytorch/torch/csrc/utils/tensor_numpy.cpp:141.)\n",
            "  return torch.from_numpy(parsed.astype(m[2], copy=False)).view(*s)\n"
          ],
          "name": "stderr"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "Oh-XVKan-g2q"
      },
      "source": [
        "val_fmnist = datasets.FashionMNIST(data_folder, download=True, train=False)\n",
        "val_images = val_fmnist.data\n",
        "val_targets = val_fmnist.targets"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "QAtH6m0e-iKd"
      },
      "source": [
        "import matplotlib.pyplot as plt\n",
        "%matplotlib inline\n",
        "import numpy as np\n",
        "from torch.utils.data import Dataset, DataLoader\n",
        "import torch\n",
        "import torch.nn as nn\n",
        "device = 'cuda' if torch.cuda.is_available() else 'cpu'"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "1a6Ft27b-jTW"
      },
      "source": [
        "class FMNISTDataset(Dataset):\n",
        "    def __init__(self, x, y):\n",
        "        x = x.float()\n",
        "        x = x.view(-1,28*28)/255\n",
        "        self.x, self.y = x, y \n",
        "    def __getitem__(self, ix):\n",
        "        x, y = self.x[ix], self.y[ix] \n",
        "        return x.to(device), y.to(device)\n",
        "    def __len__(self): \n",
        "        return len(self.x)\n",
        "\n",
        "from torch.optim import SGD, Adam\n",
        "def get_model():\n",
        "    model = nn.Sequential(\n",
        "        nn.Linear(28 * 28, 1000),\n",
        "        nn.ReLU(),\n",
        "        nn.Linear(1000, 10)\n",
        "    ).to(device)\n",
        "\n",
        "    loss_fn = nn.CrossEntropyLoss()\n",
        "    optimizer = Adam(model.parameters(), lr=1e-3)\n",
        "    return model, loss_fn, optimizer\n",
        "\n",
        "def train_batch(x, y, model, opt, loss_fn):\n",
        "    model.train()\n",
        "    prediction = model(x)\n",
        "    batch_loss = loss_fn(prediction, y)\n",
        "    batch_loss.backward()\n",
        "    optimizer.step()\n",
        "    optimizer.zero_grad()\n",
        "    return batch_loss.item()\n",
        "\n",
        "def accuracy(x, y, model):\n",
        "    model.eval()\n",
        "    # this is the same as @torch.no_grad \n",
        "    # at the top of function, only difference\n",
        "    # being, grad is not computed in the with scope\n",
        "    with torch.no_grad():\n",
        "        prediction = model(x)\n",
        "    max_values, argmaxes = prediction.max(-1)\n",
        "    is_correct = argmaxes == y\n",
        "    return is_correct.cpu().numpy().tolist()"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "TV6g7C3v-k62"
      },
      "source": [
        "def get_data(): \n",
        "    train = FMNISTDataset(tr_images, tr_targets) \n",
        "    trn_dl = DataLoader(train, batch_size=32, shuffle=True)\n",
        "    val = FMNISTDataset(val_images, val_targets) \n",
        "    val_dl = DataLoader(val, batch_size=len(val_images), shuffle=False)\n",
        "    return trn_dl, val_dl"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "6O1wjRFi-mFG"
      },
      "source": [
        "@torch.no_grad()\n",
        "def val_loss(x, y, model):\n",
        "    prediction = model(x)\n",
        "    val_loss = loss_fn(prediction, y)\n",
        "    return val_loss.item()"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "fNzWYrew-ndP"
      },
      "source": [
        "trn_dl, val_dl = get_data()\n",
        "model, loss_fn, optimizer = get_model()"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "-rKvZEha-ooh",
        "outputId": "1f853a8c-83da-4500-d334-5f2090d3973a",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 145
        }
      },
      "source": [
        "from torch import optim\n",
        "scheduler = optim.lr_scheduler.ReduceLROnPlateau(optimizer, factor=0.5, patience=0, threshold = 0.001, verbose=True, min_lr = 1e-5, threshold_mode = 'abs')\n",
        "train_losses, train_accuracies = [], []\n",
        "val_losses, val_accuracies = [], []\n",
        "for epoch in range(30):\n",
        "    #print(epoch)\n",
        "    train_epoch_losses, train_epoch_accuracies = [], []\n",
        "    for ix, batch in enumerate(iter(trn_dl)):\n",
        "        x, y = batch\n",
        "        batch_loss = train_batch(x, y, model, optimizer, loss_fn)\n",
        "        train_epoch_losses.append(batch_loss) \n",
        "    train_epoch_loss = np.array(train_epoch_losses).mean()\n",
        "\n",
        "    for ix, batch in enumerate(iter(trn_dl)):\n",
        "        x, y = batch\n",
        "        is_correct = accuracy(x, y, model)\n",
        "        train_epoch_accuracies.extend(is_correct)\n",
        "    train_epoch_accuracy = np.mean(train_epoch_accuracies)\n",
        "\n",
        "    for ix, batch in enumerate(iter(val_dl)):\n",
        "        x, y = batch\n",
        "        val_is_correct = accuracy(x, y, model)\n",
        "        validation_loss = val_loss(x, y, model)\n",
        "        scheduler.step(validation_loss)\n",
        "    val_epoch_accuracy = np.mean(val_is_correct)\n",
        "\n",
        "    train_losses.append(train_epoch_loss)\n",
        "    train_accuracies.append(train_epoch_accuracy)\n",
        "    val_losses.append(validation_loss)\n",
        "    val_accuracies.append(val_epoch_accuracy)"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "Epoch     2: reducing learning rate of group 0 to 5.0000e-04.\n",
            "Epoch     8: reducing learning rate of group 0 to 2.5000e-04.\n",
            "Epoch    11: reducing learning rate of group 0 to 1.2500e-04.\n",
            "Epoch    14: reducing learning rate of group 0 to 6.2500e-05.\n",
            "Epoch    15: reducing learning rate of group 0 to 3.1250e-05.\n",
            "Epoch    16: reducing learning rate of group 0 to 1.5625e-05.\n",
            "Epoch    17: reducing learning rate of group 0 to 1.0000e-05.\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "lX0dSmyE_GSm",
        "outputId": "3d8e1c75-6ca3-4bc0-eca3-7fd328e47ab3",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 337
        }
      },
      "source": [
        "epochs = np.arange(30)+1\n",
        "import matplotlib.ticker as mtick\n",
        "import matplotlib.pyplot as plt\n",
        "import matplotlib.ticker as mticker\n",
        "%matplotlib inline\n",
        "plt.subplot(211)\n",
        "plt.plot(epochs, train_losses, 'bo', label='Training loss')\n",
        "plt.plot(epochs, val_losses, 'r', label='Validation loss')\n",
        "plt.gca().xaxis.set_major_locator(mticker.MultipleLocator(1))\n",
        "plt.title('Training and validation loss with learning rate scheduler')\n",
        "plt.xlabel('Epochs')\n",
        "plt.ylabel('Loss')\n",
        "plt.legend()\n",
        "plt.grid('off')\n",
        "plt.show()\n",
        "plt.subplot(212)\n",
        "plt.plot(epochs, train_accuracies, 'bo', label='Training accuracy')\n",
        "plt.plot(epochs, val_accuracies, 'r', label='Validation accuracy')\n",
        "plt.gca().xaxis.set_major_locator(mticker.MultipleLocator(1))\n",
        "plt.title('Training and validation accuracy with learning rate scheduler')\n",
        "plt.xlabel('Epochs')\n",
        "plt.ylabel('Accuracy')\n",
        "plt.gca().set_yticklabels(['{:.0f}%'.format(x*100) for x in plt.gca().get_yticks()]) \n",
        "plt.legend()\n",
        "plt.grid('off')\n",
        "plt.show()"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "539Fi1Kw_1-n"
      },
      "source": [
        ""
      ],
      "execution_count": null,
      "outputs": []
    }
  ]
}